Uniqueness of spaces pretangent to metric spaces at infinity
We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It...
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| Veröffentlicht in: | Український математичний вісник |
|---|---|
| Datum: | 2019 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russian |
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Інститут прикладної математики і механіки НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/169432 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ. |
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Dovgoshey, O. Bilet, V. 2020-06-13T08:23:45Z 2020-06-13T08:23:45Z 2019 Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ. 1810-3200 2010 MSC. 54E35 https://nasplib.isofts.kiev.ua/handle/123456789/169432 We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It is also shown that the uniqueness of pretangent spaces to subsets of a real line is closely related to the “asymptotic asymmetry” of these subsets. ru Інститут прикладної математики і механіки НАН України Український математичний вісник Uniqueness of spaces pretangent to metric spaces at infinity Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Uniqueness of spaces pretangent to metric spaces at infinity |
| spellingShingle |
Uniqueness of spaces pretangent to metric spaces at infinity Dovgoshey, O. Bilet, V. |
| title_short |
Uniqueness of spaces pretangent to metric spaces at infinity |
| title_full |
Uniqueness of spaces pretangent to metric spaces at infinity |
| title_fullStr |
Uniqueness of spaces pretangent to metric spaces at infinity |
| title_full_unstemmed |
Uniqueness of spaces pretangent to metric spaces at infinity |
| title_sort |
uniqueness of spaces pretangent to metric spaces at infinity |
| author |
Dovgoshey, O. Bilet, V. |
| author_facet |
Dovgoshey, O. Bilet, V. |
| publishDate |
2019 |
| language |
Russian |
| container_title |
Український математичний вісник |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
We find the necessary and sufficient conditions under which an unbounded metric space X has, at infinity, a unique pretangent space Ωˣ∞, ř for every scaling sequence ř. In particular, it is proved that Ωˣ∞, ř is unique and isometric to the closure of X for every logarithmic spiral X and every ř. It is also shown that the uniqueness of pretangent spaces to subsets of a real line is closely related to the “asymptotic asymmetry” of these subsets.
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| issn |
1810-3200 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/169432 |
| citation_txt |
Uniqueness of spaces pretangent to metric spaces at infinity / O. Dovgoshey, V. Bilet // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 57-87. — Бібліогр.: 12 назв. — англ. |
| work_keys_str_mv |
AT dovgosheyo uniquenessofspacespretangenttometricspacesatinfinity AT biletv uniquenessofspacespretangenttometricspacesatinfinity |
| first_indexed |
2025-11-30T13:44:32Z |
| last_indexed |
2025-11-30T13:44:32Z |
| _version_ |
1850857774740668416 |